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Cheating-immune secret sharing schemes from codes and cumulative arrays

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Abstract

A cheating-immune secret sharing scheme prevents a cheater, who submits a corrupted share, from gaining an advantage in knowing the secret over the honest participants. We revisit two methods, that uses linear codes, to construct Boolean functions satisfying multiple cryptographic criteria. We show that these methods can be used to build new cheating-immune (n, n)-secret sharing schemes. We also revisit two general constructions of secret sharing schemes using cumulative arrays and apply them to build cheating-immune (t, n)-threshold secret sharing schemes.

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Acknowledgements

This research is supported in part by the National Research Foundation Singapore under the Competitive Research Programme (NRF-CRP2-2007-03). The work of R. dela Cruz is supported in part by the NTU PhD Research Scholarship. He would like to thank Somphong Jitman for some helpful discussions. The authors would like to thank the reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Romar dela Cruz & Huaxiong Wang

  2. Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines

    Romar dela Cruz

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  1. Romar dela Cruz
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  2. Huaxiong Wang
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Correspondence to Romar dela Cruz.

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dela Cruz, R., Wang, H. Cheating-immune secret sharing schemes from codes and cumulative arrays. Cryptogr. Commun. 5, 67–83 (2013). https://doi.org/10.1007/s12095-012-0076-4

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